Numericals on Dual Problem of Linear Programming


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 (Dual Problem)

 

1.        Write the dual of

Maximize     Z = 5x1 + 3x2

Subject to    x1 + x2 \< 2

5x1 + 2x2 \< 10

3x1 + 8x2 \< 12

x1, x2  \<0                                     (Ans :  Minimize Z*= 2y1 + 10y2 + 12y3

Subject to          y1 + 5y2 + 8y3

5x1 + 2x2  10

y1 y2 y3  >/0)

2.        Write the dual of

Maximize     Z = 4x1 + 3x2

Subject to    3x1 + 2x2 \< 15

2x1 + 5x2  \<20

x1, x2  >/0                                        (Ans :  Minimize Z* = 15y1 – 20y2

Subject to          3y1 + 2y2 >/ 4

5x1 + 2x2  >/10

2y1 + 5y2 >/3

y1 y2  >/0)

 

3.        Solve the following LPP using dual and interpret the optimal solution.

Minimize      Z = x1 + x2

Subject to    0.12x1 + 0.04x2  >/600

0.10x1 + 0.40x2 >/ 1000

x1, x2 >/ 0                                      (Ans :  x1 = 50000/11, x2 = 15000/11)

 

4.        Minimize Z = 120x1 + 180x2

Subject to    6x1 + 3x2  >/45

4x1 + 10x2 >/ 55

x1, x2  >/0

(a)      Write the dual of the given lpp.

(b)      Find dual optimal solution.

(c)      Mention unutilized capacity of slack variables if any.

(d)      State with reasons whether degeneracy occurs in the sum.

 


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